Journal of Intelligent & Fuzzy Systems 15 (2004) 149-164
IOS Press
Quaternion neural network with geometrical operators


Nobuyuki Matsui a,*, Teijiro Isokawaa a, Hiromi Kusamichi a, Ferdinand Peper a,b and
Haruhiko Nishimura c
a Division of Computer Engineering, University of Hyogo, 2167 Shosha, Himeji, 671-2201 Japan
b Nanotechnology Group, National Institute of Information and Communications Technology, 588-2 iwaoka,
Iwaoka-cho, Nishi-ku, Kobe, 651-2401 Japan
c Graduate School of Applied lnformatics, University of Hyogo, 1-3-3 Higashikawasaki-cho, Chuo-ku,Kobe, 650-0044 Japan

Abstract. Quaternion neural networks are models in which computations ot the neurons are based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in three-dimensiona1 space, as well as in color space for an image compression problem, whereas realvalued BP algorithms fail. The quaternion neural network also performs superior in terms of convergence speed to a real-valued neural network with respect to the 3-bit parity check problem, as simulations show.